Answer
$\sum\limits_{k=1}^{\infty }{6k\text{ }}$
Work Step by Step
$6+12+18+24+\ldots $
This can be written as,
$6\cdot 1+6\cdot 2+6\cdot 3+6\cdot 4+\ldots $
This is the sum of the positive multiples of $6$, and the value of $k$ varies from $k=1$ to $k=\infty $,
Thus, the sigma notation is,
$\sum\limits_{k=1}^{\infty }{6k}$
Thus, the sigma notation for the sum $6+12+18+24+\ldots $ is$\sum\limits_{k=1}^{\infty }{6k\text{ }}$.
